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A136233 Matrix square of triangle U = A136228, read by rows.

%I A136233 #2 Mar 30 2012 18:37:08
%S A136233 1,2,1,10,8,1,75,76,14,1,753,888,196,20,1,9534,12542,3087,370,26,1,
%T A136233 146353,209506,55552,7320,598,32,1,2647628,4058806,1136975,159645,
%U A136233 14235,880,38,1,55251994,89706276,26224597,3856065,364403,24480,1216,44,1
%N A136233 Matrix square of triangle U = A136228, read by rows.
%F A136233 Column k of U^2 (this triangle) = column 1 of P^(3k+1), where P = triangle A136220.
%e A136233 This triangle, U^2, begins:
%e A136233 1;
%e A136233 2, 1;
%e A136233 10, 8, 1;
%e A136233 75, 76, 14, 1;
%e A136233 753, 888, 196, 20, 1;
%e A136233 9534, 12542, 3087, 370, 26, 1;
%e A136233 146353, 209506, 55552, 7320, 598, 32, 1;
%e A136233 2647628, 4058806, 1136975, 159645, 14235, 880, 38, 1;
%e A136233 55251994, 89706276, 26224597, 3856065, 364403, 24480, 1216, 44, 1; ...
%e A136233 where column 0 of U^2 = column 1 of P = A136220.
%o A136233 (PARI) {T(n,k)=local(P=Mat(1),U=Mat(1),PShR);if(n>0,for(i=0,n, PShR=matrix(#P,#P, r,c, if(r>=c,if(r==c,1,if(c==1,0,P[r-1,c-1]))));U=P*PShR^2; U=matrix(#P+1, #P+1, r,c, if(r>=c, if(r<#P+1,U[r,c], if(c==1,(P^3)[ #P,1],(P^(3*c-1))[r-c+1,1])))); P=matrix(#U, #U, r,c, if(r>=c, if(r<#R,P[r,c], (U^c)[r-c+1,1])))));(U^2)[n+1,k+1]}
%Y A136233 Cf. A136222 (column 0); related tables: A136220 (P), A136228 (U), A136230 (V), A136231 (W=P^3), A136236 (U^3).
%K A136233 nonn,tabl
%O A136233 0,2
%A A136233 _Paul D. Hanna_, Feb 07 2008